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My math teacher asked the question:

The three sides of a triangle and the four sides of a quadrilateral can intersect each other at most $x$ points if this number is finite. What is $x$?

I wasn't sure at the beginning, but then after pondering a lot and looking at this website on brainly.com (sorry Stack Exchange fans 😊) I came with the conclusion that $8$ was the maximum. However, I have got no clue how to solve this!!! Even after putting it to test on GeoGebra, I still haven't managed to make a firm proof on this topic.

Any help would be immensely appreciated ヾ(•ω•`)

GeoGebra picture
(the GeoGebra graph)

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    $\begingroup$ Here's an idea: each side of the quadrilateral must be straight. At most, how many times can a single straight line intersect the sides of a triangle? You have four sides to work with, does this help get you started? $\endgroup$
    – Jake Brown
    May 13, 2021 at 15:50
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    $\begingroup$ Similar : math.stackexchange.com/q/2708006 $\endgroup$
    – Jean Marie
    May 13, 2021 at 15:53
  • $\begingroup$ Yes @JeanMarie I have seen that thanks but it wasn't really too close to mine ;) $\endgroup$
    – Arale
    May 13, 2021 at 15:56
  • $\begingroup$ Thank you @JakeBrown this helps a lot!👍 $\endgroup$
    – Arale
    May 13, 2021 at 15:58

2 Answers 2

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Hint: Show a line segment cannot intersect the interiors of all three edges of a triangle.

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Okay, so this is my final answer, thanks everyone for your advice :)

If there's anything wrong please let me know!

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